RCR-AF: Enhancing Model Generalization via Rademacher Complexity Reduction Activation Function

• URL: http://arxiv.org/abs/2507.22446v1
• Date: Wed, 30 Jul 2025 07:45:03 GMT
• Title: RCR-AF: Enhancing Model Generalization via Rademacher Complexity Reduction Activation Function
• Authors: Yunrui Yu, Kafeng Wang, Hang Su, Jun Zhu,
• Abstract summary: This paper investigates activation functions as a crucial yet underexplored component for enhancing model robustness.<n>We propose a Rademacher Complexity Reduction Activation Function (RCR-AF), a novel activation function designed to improve both generalization and adversarial resilience.
• Score: 28.98307539597017
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Despite their widespread success, deep neural networks remain critically vulnerable to adversarial attacks, posing significant risks in safety-sensitive applications. This paper investigates activation functions as a crucial yet underexplored component for enhancing model robustness. We propose a Rademacher Complexity Reduction Activation Function (RCR-AF), a novel activation function designed to improve both generalization and adversarial resilience. RCR-AF uniquely combines the advantages of GELU (including smoothness, gradient stability, and negative information retention) with ReLU's desirable monotonicity, while simultaneously controlling both model sparsity and capacity through built-in clipping mechanisms governed by two hyperparameters, $\alpha$ and $\gamma$. Our theoretical analysis, grounded in Rademacher complexity, demonstrates that these parameters directly modulate the model's Rademacher complexity, offering a principled approach to enhance robustness. Comprehensive empirical evaluations show that RCR-AF consistently outperforms widely-used alternatives (ReLU, GELU, and Swish) in both clean accuracy under standard training and in adversarial robustness within adversarial training paradigms.

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